These verses, cited by Herodotus 2.116.1–117.1 derive from a narrative tradition that indicates more than one stopover for Paris=Alexandros and Helen after her abduction/elopement from Sparta. I epitomize here from HPC 75–79 [= I§§184–187]]:
Herodotus makes a point of distinguishing Homer from what he describes as the poet of the Cypria, and, in making this distinction, he actually quotes a passage from the Homeric Iliad to prove his point (Herodotus 2.116.1–2.117.1):
Δοκέει δέ μοι καὶ ῞Ομηρος τὸν λόγον τοῦτον πυθέσθαι· ἀλλ’, οὐ γὰρ ὁμοίως ἐς τὴν ἐποποιίην εὐπρεπὴς ἦν τῷ ἑτέρῳ τῷ περ ἐχρήσατο, [ἐς ὃ] μετῆκε αὐτόν, δηλώσας ὡς καὶ τοῦτον ἐπίσταιτο τὸν λόγον. Δῆλον δέ, κατά περ ἐποίησε ἐν Ἰλιάδι (καὶ οὐδαμῇ ἄλλῃ ἀνεπόδισε ἑωυτόν) πλάνην τὴν Ἀλεξάνδρου, ὡς ἀπηνείχθη ἄγων Ἑλένην τῇ τε δὴ ἄλλῃ πλαζόμενος καὶ ὡς ἐς Σιδῶνα τῆς Φοινίκης ἀπίκετο. Ἐπιμέμνηται δὲ αὐτοῦ ἐν Διομήδεος Ἀριστηίῃ· λέγει δὲ τὰ ἔπεα ὧδε·
ἔνθ’ ἔσαν οἱ πέπλοι παμποίκιλοι, ἔργα γυναικῶν
Σιδονίων, τὰς αὐτὸς Ἀλέξανδρος θεοειδὴς
ἤγαγε Σιδονίηθεν, ἐπιπλὼς εὐρέα πόντον,
τὴν ὁδὸν ἣν Ἑλένην περ ἀνήγαγεν εὐπατέρειαν.
[I.06.289–292]
Ἐπιμέμνηται δὲ καὶ ἐν Ὀδυσσείῃ ἐν τοῖσδε τοῖσι ἔπεσι·
τοῖα Διὸς θυγάτηρ ἔχε φάρμακα μητιόεντα,
ἐσθλά, τά οἱ Πολύδαμνα πόρεν Θῶνος παράκοιτις
Αἰγυπτίη, τῇ πλεῖστα φέρει ζείδωρος ἄρουρα
φάρμακα, πολλὰ μὲν ἐσθλὰ μεμιγμένα, πολλὰ δὲ λυγρά.
[O.04.227–230]
Καὶ τάδε ἕτερα πρὸς Τηλέμαχον Μενέλεως λέγει·
Αἰγύπτῳ μ’ ἔτι δεῦρο θεοὶ μεμαῶτα νέεσθαι
ἔσχον, ἐπεὶ οὔ σφιν ἔρεξα τεληέσσας ἑκατόμβας.
[O.04.351–352]
Ἐν τούτοισι τοῖσι ἔπεσι δηλοῖ ὅτι ἠπίστατο τὴν ἐς Αἴγυπτον Ἀλεξάνδρου πλάνην· ὁμουρέει γὰρ ἡ Συρίη Αἰγύπτῳ, οἱ δὲ Φοίνικες, τῶν ἐστι ἡ Σιδών, ἐν τῇ Συρίῃ οἰκέουσι. Κατὰ ταῦτα δὲ τὰ ἔπεα καὶ τόδε [τὸ χωρίον] οὐκ ἥκιστα ἀλλὰ μάλιστα δηλοῖ ὅτι οὐκ Ὁμήρου τὰ Κύπρια ἔπεά ἐστι ἀλλ’ ἄλλου τινός· ἐν μὲν γὰρ τοῖσι Κυπρίοισι εἴρηται ὡς τριταῖος ἐκ Σπάρτης Ἀλέξανδρος ἀπίκετο ἐς τὸ Ἴλιον ἄγων Ἑλένην, εὐαέϊ τε πνεύματι χρησάμενος καὶ θαλάσσῃ λείῃ· ἐν δὲ Ἰλιάδι λέγει ὡς ἐπλάζετο ἄγων αὐτήν. Ὅμηρος μέν νυν καὶ τὰ Κύπρια ἔπεα χαιρέτω.
I think that Homer was aware of this story [= the story of Helen in Egypt]. But, because it [= this story] was not as appropriate for epic composition as was the other one [= the other story] that he used, he omitted it, though he made it clear that he was aware of this story [= the story of Helen in Egypt] as well. It is clear on the basis of the way he composed in the Iliad (and nowhere else has he [= Homer] retraced his steps to this) the detour of Alexandros [= Paris]—how he [= Paris], as he was bringing Helen, was blown off course and was detoured in various places and then how he reached Sidon in Phoenicia. He [= Homer] mentions the story [of Helen in Egypt] in the part about the greatest deeds of Diomedes. And the epic words he says are as follows.
There they were, the peploi, completely pattern-woven [poikiloi], the work of women
from Sidon, whom Alexandros [= Paris] himself, the godlike,
had brought home [to Troy] from the land of Sidon, sailing over the vast sea,
on the very same journey as the one he took when he brought back home [to Troy] also Helen, the one who is descended from the most noble father.
[I.06.289–292]
He [= Homer] mentions it [= the story of Helen in Egypt] in the Odyssey also, in these epic words:
Such magical things she had, the daughter of Zeus,
things of good outcome, which to her did Polydamna give, wife of Thon.
She was Egyptian. For her, many were the things produced by the life-giving earth,
magical things—many good mixtures and many baneful ones.
[O.04.227–230]
And these other things are said to Telemachus by Menelaos:
I was eager to return here, but the gods still held me in Egypt,
Since I had not sacrificed entire hecatombs [hekatombai] to them.
[O.04.351–352]
In these epic verses the Poet makes clear that he knew of the detour of Alexandros [= Paris] to Egypt; for Syria borders on Egypt, and the Phoenicians whose territory is Sidon dwell in Syria. In terms of these epic verses, this shows most clearly that the epic of the Cypria is not by Homer but by someone else. For in the Cypria it is said that on the third day after setting sail from Sparta Alexandros [= Paris] arrived in Troy bringing Helen, having made good use of a favorable wind and smooth seas. In the Iliad, on the other hand, he [= Homer] says that he [= Paris] was detoured as he was bringing her [= Helen]. So much for Homer and the epic of the Cypria.
(A note on Herodotus 2.116.4–5.) I question the judgment of modern editors who bracket sections 4 and 5 of Herodotus 2.116. Granted, the topic in these sections is the detour of Menelaos and Helen in Egypt after the war at Troy, not the detour of Paris and Helen before the war. But these passages are relevant to what Herodotus says thereafter (2.118–119) about Helen in Egypt after the war. Herodotus is making the point that there are other Homeric stories about Helen in Egypt, whereas there are no other Homeric stories about Helen in Phoenicia.
I now offer a paraphrase of the arguments made by Herodotus here at 2.116.1–2.117.1:
In a non-Homeric version of an epic called the Cypria (a version known to Herodotus but not to us), it is said that Paris and Helen sailed to Troy without making any detour. There is an alternative version in the Homeric Iliad, and Herodotus quotes the relevant verses. In this version, it is said that Paris and Helen did make a detour: they went to Phoenicia before they went to Troy. On the basis of an Egyptian story about Paris and Helen, Herodotus goes on to argue that they went to Egypt as well as Phoenicia, and that Homer knew it. After all, Egypt is next to Phoenicia. But the problem is, Homer later elided the story of Helen in Egypt as inappropriate. So the Iliad tells the story about Helen in Troy, not the story about Helen in Egypt. And the Odyssey follows the Iliad in accepting the story of Helen in Troy. Both epics, however, show traces of the story of Helen in Egypt, though the traces in the Iliad are only indirect.
Next, I offer a critical analysis of this paraphrase:
Herodotus considers the stories about detours in Egypt and Phoenicia within the larger context of stories about Helen in Egypt. Upon retelling an Egyptian version of a story about a detour of Paris and Helen in Egypt after he abducted her from Sparta (2.112–115), Herodotus says that Homer must have known that story (2.116.1). Then, in order to show that this is so, Herodotus offers proof (2.116–117), quoting I.06.289–292 and O.04.227–230 together with O.04.351–352. The passage I.06.289–292 concerns the detour of Paris and Helen before the war at Troy while the passages O.04.227–230 and O.04.351–352 concern the detour of Menelaos and Helen after the war. The first passage is meant as indirect proof that the story of Helen in Egypt was recognized by Homer in the Iliad while the other two passages are meant as direct proof that the story of Helen in Egypt was recognized by Homer in the Odyssey. The passages from the Odyssey are relevant to what Herodotus goes on to argue about the story of Helen in Egypt: he finds that this story is more believable than the story of Helen in Troy (2.118–119). In the Egyptian version, Paris is forced to leave Helen behind in Egypt after the two of them are detoured there (2.115.5). That is where Menelaos finds her after the war. According to this Egyptian version, then, Helen never went to Troy. For Herodotus, this version makes more sense than the Homeric version that dominates the Iliad and Odyssey.
I conclude by considering again the fact that Herodotus distinguishes Homer as the poet of the Iliad from the poet of the Cypria. This fact shows that the historian is familiar with the Panathenaic Homer. That is, he thinks of Homer as the poet of the two epics performed at the Panathenaia, the Iliad and the Odyssey. Nevertheless, Herodotus does not presuppose that everyone thinks this way. That is why he makes a point of establishing the distinction in the first place. He speaks of the poet of the Cypria as someone who may be considered to be Homer by others, but Herodotus knows better.